Why do they converge as average life of MBS decreases and diverge as the MBS average life increases? Can anyone explain?

The greater the average life, the more opportunities there are to exercise the option; hence, the option value increases as the average life increases.

If there were only one month left in the mortgages, how many prepayments would you expect? I’d hazard to guess it’d be very few.

True. But doesn’t z spread and nominal spread both include prepayment risk? So if value of prepayment option decreases (the prepayment risk decreases in this case), shouldn’t the difference between z spread and nominal spread stays the same instead of diverging/converging?

My mistake: I misread the question. I was thinking Z-spread and OAS.

OK, now the brain’s functioning: remember that the nominal spread is a spread at one point on the par yield curve while the Z-spread is a spread added to the entire spot curve. As the maturity shortens, the difference between the YTM and the average spot rate generally decreases, so for the Z-spread you’re adding the spread to a curve that is getting closer to (has less dispersion around) the YTM. As an example – sort of like the example I (mistakenly) cited above) – with one month left, the YTM and the spot rate are the same, so the nominal spread has to equal the Z-spread. With 120 months left, the spot rates could have considerable dispersion around the YTM; that’s why the Z-spread and the nominal spread are different.

If you think of the nomimal spread as a spread added to every point of a _ **flat** _ par curve, then it becomes clearer: with a long maturity, the spot curve can be very different from a flat curve; with a short maturity, it cannot be nearly so different.

Ah-ha, now it makes sense, thanks!

Whew!

You’re welcome.